Fekete-Szegö and Hankel inequalities for certain class of analytic functions related to the sine function
In this present investigation, the authors obtain Fekete-Szegö inequality for certain normalized analytic function $ f(\zeta) $ defined on the open unit disk for which $ (f'(\zeta)^{\vartheta}\left( \frac{\zeta f'(\zeta )}{f(\zeta )}\right)^{1-\vartheta} \prec 1+\sin \zeta ; \qquad (0\l...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-01-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022354?viewType=HTML |
| Summary: | In this present investigation, the authors obtain Fekete-Szegö inequality for certain normalized analytic function $ f(\zeta) $ defined on the open unit disk for which
$ (f'(\zeta)^{\vartheta}\left( \frac{\zeta f'(\zeta )}{f(\zeta )}\right)^{1-\vartheta} \prec 1+\sin \zeta ; \qquad (0\leq \vartheta \leq 1) $
lies in a region starlike with respect to $ 1 $ and symmetric with respect to the real axis. As a special case of this result, the Fekete-Szegö inequality for a class of functions defined through Poisson distribution series is obtained. Further, we discuss the second Hankel inequality for functions in this new class. |
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| ISSN: | 2473-6988 |